A SINR Maximizing Interpolation-and-Decimation-based Dimensionality Reduction Technique, with Application to Beamforming
We present a dimensionality reduction technique based on a joint interpolation and decimation scheme, with application to beamforming. The dimensionality reduction is achieved by a two step procedure: interpolation followed by decimation. The array snapshots are interpolated by a ﬁnite impulse response (FIR) ﬁlter in order to generate correlation between its samples. The decimation stage then discards some samples from the correlated interpolator output signal, effectively reducing the snapshots’ length. A notable point of this technique is the elegant and effective way to design the interpolation ﬁlter. The design is such that, for a given decimation pattern, the interpolation ﬁlter maximizes the signal-to-interference-and-noise ratio (SINR) at the ouput of the decimation stage. The optimization of the reduced dimensionality stage is made independently of the ﬁnal application ﬁltering stage, allowing the proposed scheme to be combined with any interference-suppressive or detection ﬁlter of choice. Investigation of this technique in light of the particularities of the beamforming signal model led to, here proposed, simpliﬁcations that allowed for a signiﬁcant reduction of its overall complexity. Comparison with renowned robust rank reduction techniques show that the proposed approach has an excellent SINR loss ﬁgure of merit performance with superior robustness and low computational complexity.
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